1. The problem is to understand the expression $\bar{x} = \sum_{i=1}^N x_i$. 2. This expression represents the sum of all values $x_i$ from $i=1$ to $i=N$. 3. The summation symbol $\sum$ means to add all terms $x_i$ where $i$ runs from 1 to $N$. 4. So, $\bar{x}$ is the total sum of the $N$ values $x_1, x_2, \ldots, x_N$. 5. Note that $\bar{x}$ here is not the average (mean) unless you divide by $N$; the average is $\frac{1}{N} \sum_{i=1}^N x_i$. 6. In summary, $\bar{x} = \sum_{i=1}^N x_i = x_1 + x_2 + \cdots + x_N$ is the sum of all $N$ values.